Heaps and heapsort on secondary storage

AbstractA heap structure designed for secondary storage is suggested that tries to make the best use of the available buffer space in primary memory. The heap is a complete multi-way tree, with multi-page blocks of records as nodes, satisfying a generalized heap property. A special feature of the tree is that the nodes may be partially filled, as in B-trees. The structure is complemented with priority-queue operations insert and delete-max. When handling a sequence of S operations, the number of page transfers performed is shown to be O(∑i = 1S(1P) log(MP)(NiP)), where P denotes the number of records fitting into a page, M the capacity of the buffer space in records, and Ni, the number of records in the heap prior to the ith operation (assuming P ⩾ 1 and S > M ⩾ c · P, where c is a small positive constant). The number of comparisons required when handling the sequence is O(∑i = 1S log2 Ni). Using the suggested data structure we obtain an optimal external heapsort that performs O((NP) log(MP)(NP)) page transfers and O(N log2 N) comparisons in the worst case when sorting N records

Scalable Visual Hierarchy Exploration

. Modern computer applications, from business decision support to scientific data analysis, utilize visualization techniques to support exploratory activities. However, most existing visual exploration tools do not scale well for large data sets, i.e., the level of cluttering on the screen is typically unacceptable and the performance is poor. To solve the cluttered interface problem, visualization tools have recently been extended to support hierarchical views of the data, with support for focusing and drilling-down using interactive brushes. To solve the scalability problem, we now investigate how best to couple such a near real-time responsive visualization tool with a database management system. This integration must be done carefully, since the direct implementation of the visual user interactions on hierarchical datasets corresponds to recursive query processing and thus is highly inefficient. For this problem, we have developed a tree labeling method, called MinMax ..

The external heapsort

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman